Question

Your test scores in one class are 80 and 88. What possible scores can you earn on your next test to have a test average between 84 and 89​, ​inclusive?

Answer 1

The average of your two scores to date is 84. You need the average of these two tests plus the next test to be between 84 and 89.

So, you need to solve for x, where 2/384 + 1/3x = 84. This will give you the lower end of your next test.

And you need to solve for y, where 2/384 + 1/3y= 89. This will give you the higher end of your next test.

The reason for the 2/3 in front of the 84 is because there are two tests there, and the reason for 1/3 in front of the unknowns is because that is just one test. Averages need to be weighted by number of observations.

I won't go through the algebra here, but the answers will be 84 and 99.

Explanation:

Answer 2

84 to 99

Explanation:

If the goal for your average is 84, then your test scores total ...

(80-84) +(88-84) = -4 +4 = 0

relative to your desired average. This means your minimum score on the next test will need to be 84 -0 = 84.

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If the goal for your average is 89, then your test scores total ...

(80-89) +(88-89) = -9 -1 = -10

relative to your desired average. This means your maximum score on the next test will need to be 89 -(-10) = 99.

To ensure a test average between 84 and 89, your next test score must be between 84 and 99.